Name: ________________________________________
Date: ______________________
Houston, We Have a Problem! Lesson –
Rocket Calculation Worksheet
Pick a rocket and engine to achieve a maximum height of 100 meters.
Check your values every 5 calculations with your teacher to make sure you are on track.
1. 𝑚𝑏 = 𝑚𝑅 + 𝑚𝐸 − 𝑚𝑝 /2
Note: make sure to use units of kilograms, not grams.
mb is the average mass of the rocket during the boost stage. (kg)
mRocket is in the rocket table (kg)
mEngine is in the engine table (initial mass with propellant) (kg)
mpropellant is in the engine table (propellant mass) and the ½ factor in the equation is the
averages the propellant for the boost stage. (kg)
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2. 𝑘 = 2 ∗ ρ ∗ Cd ∗ A k is the air drag constant (kg/m)
Cd = 0.75, the drag coefficient for an average rocket (has no units)
ρ = air density = 1.223 kg/m3
A is the cross-sectional area of the rocket (m2).
Use the diameter of the rocket in the rocket table to calculate the area.
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τ = thrust duration is in the engine table (s)
3. T = I / τ
I = total impulse is in the engine table (Ns) Note: This is an average impulse.
T = average motor thrust (N)
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𝑇− 𝑚𝑏 ∗𝑔
4. 𝑞 = √
𝑘
T, k, and mb calculated above
g is the acceleration of gravity at 9.81 m/s2
q is an intermediate value needed to solve future equations to ultimately determine the boost
height. (m/s)
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5. 𝑝 =
2∗𝑘∗𝑞
𝑚𝑏
k, q, and mb calculated above
p is an intermediate value needed to solve future equations to ultimately determine the boost
height. (s-1)
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Houston We Have a Problem! Lesson – Rocket Calculation Worksheet
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1−𝑒 −𝑝∗𝜏
 = thrust duration from engine table (s)
6. 𝑣𝜏 = 𝑞 ∗ 1+𝑒 −𝑝∗𝜏
𝑣𝜏 is the velocity at the end of burnout (m/s)
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7. ℎ𝑏 =
𝑚𝑏
2𝑘
𝑞2
∗ ln(𝑞2−𝑣 2)
𝜏
k, q, and mb and 𝑣𝜏 calculated above
hb = height during the boost stage (m)
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mc = mass of rocket during the costing phase (kg)
8. mc = mr + me - mp
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9. 𝑞𝑐2 =
−𝑚𝑐 ∗𝑔
k and mc calculated above, g = 9.81 m/s2
𝑘
qc2 is an intermediate value needed to solve a future equation to ultimately determine the
coast height. (m2/s2) Note: qc2 is a negative value
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10. ℎ𝑐 =
𝑚𝑐
2𝑘
∗ ln(
𝑞𝑐 2 −𝑣𝜏2
𝑞𝑐2
)
ℎ𝑐 𝑖𝑠 𝑡ℎ𝑒 𝒄𝒐𝒂𝒔𝒕𝒊𝒏𝒈 𝒉𝒆𝒊𝒈𝒉𝒕 𝑖𝑛 (𝑚)
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11. ℎ𝑇 = ℎ𝑏 + ℎ𝑐
ℎ𝑇 𝑖𝑠 𝑡ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 ℎ𝑒𝑖𝑔ℎ𝑡 𝑖𝑛 (𝑚) (restricted to 100 m, a
small soccer field, for example)
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Questions
1. What parameters are changing over the course of the flight? Is mass constant?
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2. What is the average thrust for your selected rocket? Hint: The table included in your
Rocketry Handout has total impulse and total burn time.
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Houston We Have a Problem! Lesson – Rocket Calculation Worksheet
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3. What happens if you use maximum thrust instead of average thrust?
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4. Without a parachute, estimate the time of descent and the momentum of impact from a 100 m
free fall. Note: momentum = mass*velocityat impact
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5. What forces are acting on the rocket? Draw a free body diagram for each stage. Assume a
vertical flight.
Boost
Coast
Descent
6. Why is lift not considered in these equations?
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7. Explain how rockets are governed by Newton’s three laws in your own words (not with
formulas):
a) 1st law
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Houston We Have a Problem! Lesson – Rocket Calculation Worksheet
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b) 2nd law
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c) 3rd law
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8. What parameters govern rocket height?
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9. List your engine size __________________.
10. List your rocket body selection ___________________.
11. List your calculated height. ________________.
12. List your mission purpose (make up a pretend or not so pretend mission of your own).
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Houston We Have a Problem! Lesson – Rocket Calculation Worksheet
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